<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> holds <br/> ( <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</font> iff <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[</a><span class="default"><font color="Olive" title="b2">q</font>,<font color="Olive" title="b1">p</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font> iff <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c4">F</font> =  <a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">R</font> =  <a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font>;<br/>
<div><span class="kw">hereby </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font> implies <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:12_1"/>
<span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font></span><br/><a NAME="E2:12_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T28" onmouseover="rs('borsuk_1/T28')" onmouseout="rh()">BORSUK_1:28</a></span>;<br/><a NAME="E3:12_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font></span>)</span>,<font color="Maroon" title="c2">p</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="t_0topsp.html#T4" target="_self" onmouseover="rs('t_0topsp/T4')" onmouseout="rh()">Th4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:12_1"/>
<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T19" onmouseover="rs('eqrel_1/T19')" onmouseout="rh()">EQREL_1:19</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:12"/>
<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font></span><br/>

<a NAME="E3:12"/><span class="kw">then </span>
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font></span>)</span>,<font color="Maroon" title="c3">q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font></span>)</span>,<font color="Maroon" title="c2">p</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T35" onmouseover="rs('eqrel_1/T35')" onmouseout="rh()">EQREL_1:35</a></span>;<br/>
<a NAME="E4:12"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font></span>)</span>,<font color="Maroon" title="c2">p</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="t_0topsp.html#T4" target="_self" onmouseover="rs('t_0topsp/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:12"/>
<span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="t_0topsp.html#T4" target="_self" onmouseover="rs('t_0topsp/T4')" onmouseout="rh()">Th4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
